Tracking is a crucial problem for nonlinear systems as it ensures stability and enables the system to accurately follow a desired reference signal. Using Takagi–Sugeno (T–S) fuzzy models, this paper addresses the problem of fuzzy observer and control design for a class of nonlinear systems. The Takagi–Sugeno (T–S) fuzzy models can represent nonlinear systems because it is a universal approximation. Firstly, the T–S fuzzy modeling is applied to get the dynamics of an observational system in order to estimate the unmeasurable states of an unknown nonlinear system. There are various kinds of nonlinear systems that can be modeled using T–S fuzzy systems by combining the input state variables linearly. Secondly, the T–S fuzzy systems can handle unknown states as well as parameters known to the indirect adaptive fuzzy observer. A simple feedback method is used to implement the proposed controller. As a result, the feedback linearization method allows for solving the singularity problem without using any additional algorithms. A fuzzy model representation of the observation system comprises parameters and a feedback gain. The Lyapunov function and Lipschitz conditions are used in constructing the adaptive law. This method is then illustrated by an illustrative example to prove its effectiveness with different kinds of nonlinear functions. A well-designed controller is effective and its performance index minimizes network utilization—this factor is particularly significant when applied to wireless communication systems.

跟踪对于非线性系统来说是一个至关重要的问题，因为它可以确保稳定性并使系统能够准确地跟踪所需的参考信号。本文使用 Takagi–Sugeno (T–S) 模糊模型，解决了一类非线性系统的模糊观测器和控制设计问题。 Takagi–Sugeno (T–S) 模糊模型可以表示非线性系统，因为它是通用逼近。首先，应用T-S模糊建模来获取观测系统的动力学，以估计未知非线性系统的不可测状态。通过线性组合输入状态变量，可以使用 T-S 模糊系统对各种非线性系统进行建模。其次，T-S 模糊系统可以处理未知状态以及间接自适应模糊观测器已知的参数。使用简单的反馈方法来实现所提出的控制器。因此，反馈线性化方法无需使用任何额外的算法即可解决奇点问题。观测系统的模糊模型表示包括参数和反馈增益。 Lyapunov 函数和 Lipschitz 条件用于构造自适应律。然后通过一个说明性例子说明该方法，以证明其对于不同类型的非线性函数的有效性。设计良好的控制器是有效的，其性能指标可以最大限度地减少网络利用率——当应用于无线通信系统时，这个因素尤其重要。